The conventional portable bicycle air pumps are shown in FIGS. 1 and 2. Such air pumps are detachably fastened to the bicycle frame. As shown in FIG. 1, a conventional one-stroke air pump 10 comprises a connection head 12 having a rear side which is fastened integrally with a cylinder 13. The act of pumping is brought about by a handle 14 which is pushed inwards to cause the piston to compress the air inside the cylinder 13. As illustrated in FIG. 2, a conventional two-stroke air pump 11 comprises a connection head 15 having a handle 16 which is attached to the rear side thereof. As a cylinder 17 is pushed and pulled, the piston is caused to compress the air in the cylinder 17. Such prior art air pumps 10 and 11 as described above are defective in design in that they are rigid and inflexible, and that they can not be therefore operated easily at any angle by a user.